ACT Preparation / Unit 15 ACT 1420 worked example, 60 to 90 seconds
Predicting From a Line of Best Fit
The idea
A prediction from a line of best fit takes three steps. First, read the line's equation, or two clear points on it, and identify what x and y measure. Second, check that the x-value lies inside the range of the data; if it does not, the prediction is an extrapolation. Third, substitute and interpret the result with units, as a typical value, not a certainty.
In practice
Worked example: an invented line of best fit for a town's monthly ice-cream sales, in thousands of dollars, against the month's average temperature in degrees is y = 1.2x − 30, fitted to months between 40 and 90 degrees. At 75 degrees, y = 1.2 × 75 − 30 = 60, about $60,000 in sales. The slope means each extra degree goes with about $1,200 more in monthly sales.
Where people slip
At 20 degrees, the line predicts −6, negative sales, which is impossible: an extrapolation outside the data has broken the model.
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